The 2nd AIAA Geometry and Mesh Generation Workshop is taking the qualitative out of mesh resolution by adopting a quantitative definition that will evolve as we move toward the vision of CFD in the year 2030.

When asked about the resolution of a mesh have you ever replied “Oh, it’s just a coarse mesh.”?

But coarse relative to what?

We use terms like coarse and fine as easy descriptors relative to a normal state.

But normal for what?

Each application has different requirements that may change over time as our expertise evolves and our computing capacity grows.

But change how?

Coarse, Medium, Fine – Oh My

The 3rd AIAA CFD High Lift Prediction Workshop (HiLiftPW-3) was largely a grid convergence study with mesh resolution levels defined primarily by guidelines for wall spacing, the number of mesh points across a blunt trailing edge, and a factor of 3 in total mesh size between resolution levels. Those levels were named coarse, medium, fine, and extra fine. The medium resolution mesh was generally defined as the mesh you’d use in your normal work.

So coarse is relative to medium.

Normal is for your daily work.

But there is no concept of changing over time.

A medium resolution mesh on the upper wing surface of the HL-CRM from GMGW-1.

Resolution in 2030

One of the benefits we gain by thinking about NASA’s CFD 2030 Vision Study is to take the long view, to get CFD out of what some have called a decade or so of stagnation, and think strategically about how we improve CFD’s capacity in order to achieve 2030’s goals.

And the study indicates that in 2030 a mesh with 10-100 billion cells is going to be normal and 1012 cells is just a normal part of a grid convergence study.

If 109 cells was classified as an extra-fine tet mesh for HiLiftPW-3, what the heck would you call 1012? What superlatives could be prefixed to “fine”? Ultra? Super? And how do you remember which is bigger?

In preparation for GMGW-2 the organizing committee created a resolution nomenclature that was quantifiable and takes growth over time into account.

Here are the givens.

The normal (aka medium) mesh for HiLiftPW-3 (in 2017) was about 150-200 million cells.

Relative mesh refinement between levels (e.g. medium to fine) was a factor of 3.

Mesh size would grow geometrically year over year.

Here are the results. Notice the convenient trend that every three years a mesh size drops one level (for example, a 1 billion cell mesh is 2018’s fine mesh and 2021’s medium mesh).

That’s still a lot of numbers and names, though. But if you take the log10 of each mesh resolution you end up with the mesh’s order as tabulated below.

So for 2018, an Order 8.5 mesh corresponds to what used to be called “medium” and an Order 10.5 mesh is what used to be called “hero.”

I greatly appreciate a quantitative definition of mesh resolution as well as the concept of relating such a measure to the available computing power and its change over time. Still, the quantitative measure as defined here is relative to a certain application and problem at hand. One would have to define an industry best practice for each application, so practically this can only be done for a few standard benchmark cases.
Seen in the context of grid sensitivity studies, why not relate the grid fineness to some more nondimensional measures such as a grid convergence index, or an error / uncertainty estimate? “Coarse” could then relate to a discretisation error estimate of, say, 5% (just to give an example).

You are absolutely correct. The measures defined for the workshop apply to the workshop cases which (because this is AIAA) are external aircraft simulations. And because we plan on doing those things until 2030 at least, this nomenclature was a good place to start.

Your second point pertains to fitness for a particular purpose which is another underlying aspect of what the 2030 vision is trying to achieve. We are going to get better at resolving things besides just throwing points at them. You mention a predefined level of accuracy. Other aspects will be adaptive meshing and high order meshing (as pointed out to me in an email from another reader of this post).